MaxVaR: Long Horizon Value at Risk in a Mark-to-Market Environment
Interdisciplinary Center (IDC) Herzliyah - Arison School of Business
University of California, Berkeley - Finance Group
Matthew P. Richardson
New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER)
New York University; National Bureau of Economic Research (NBER)
The standard VaR approach considers only terminal risk, completely ignoring the sample path of portfolio values. In reality interim risk may be critical in a mark-to-market environment. Sharp declines in value may generate margin calls and affect trading strategies. In this paper we introduce the notion of MaxVaR, analogous to VaR in every way except it quantifies the probability of seeing a given loss on or before the terminal date rather than at the terminal date. Under standard set of assumptions we provide a simple formula for MaxVaR and examine the ratio of MaxVaR to VaR. For reasonable parameterizations MaxVaR may exceed VaR by over 40%. MaxVaR exceeds VaR by as much as 80% or more for high Sharpe Ratio hedge-fund-like return distributions.
Number of Pages in PDF File: 9
Keywords: Value at risk, drawdown risk, long horizon risk
JEL Classification: G00
Date posted: March 26, 2004
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